Method and a device for controlling and regulating an alternating current rotating electrical machine, in particular a synchronous alternating current rotating electrical machine

ABSTRACT

A method of regulating a rotating electrical machine includes a preparatory step of determining a discrete voltage control law for the machine. The discrete control voltage to be applied at each sampling time is determined in the form of a first term corresponding to free evolution of the state of the machine in the absence of control, between the preceding sampling time and the current sampling time, and a second term dependent on the set point torque and a set point for the magnetic energy consumed by the machine. The method further includes, at each sampling time, a step of determining, with the aid of the discrete control law, the control voltage to be applied to the machine for the torque of the machine to reach the set point torque and the magnetic energy consumed by the machine to correspond to the set point magnetic energy.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a method of regulating analternating current rotating electrical machine, in particular asynchronous electric motor with smooth poles. It also relates to adevice for supplying power to an alternating current rotating electricalmachine.

[0003] It applies in particular, although not exclusively, to motorsused in rail transportation for traction and active suspension.

[0004] To be more precise, the invention relates to a regulation methodcapable of slaving the electromagnetic torque of the machine to a setpoint torque.

[0005] 2. Description of the Prior Art

[0006] The speed of a synchronous machine is generally controlled byregulating its electromagnetic torque. To this end, rotating machinesare generally provided with a regulator receiving as input a set pointelectromagnetic torque and one or more sampled signals representing theelectromagnetic torque of the machine and produced by measuring thestator current, the regulator applying a control voltage to a powersupply inverter of the machine. To slave the electromagnetic torque ofthe machine to the set point torque, at each sampling time the regulatorpredicts the torque at the next sampling time and modifies the invertercontrol voltage accordingly.

[0007] A principal concern in most industrial applications is improvingthe dynamic performance of such machines and in particular increasingthe torque dynamic range.

[0008] A first solution is to increase the switching capacity of thepower switches of the inverter in order to increase the switchingfrequency. However, this solution implies using very costly powercomponents and increases switching losses.

[0009] The system could use low-loss electronic components. This isunacceptable, however, because it considerably increases the cost of thepower supply device of the machine.

[0010] There exist methods of defining the operation of a regulatorusing a continuous time model to model the operation of the machine, tocarry out what is referred to as a “synthesis” by using the model todetermine, again in continuous time, equations yielding the correctivecontrol input to the system as a function of operating parametersrequired to obtain the specified operation, and then to convert theequations into a discrete time form to obtain differential equationsthat can be solved by a digital computer integrated into the regulator.

[0011] However, the performance of such methods is limited in terms ofcontrol dynamic range, and instability can occur if the sampling periodimposed by the inverter is too long. Also, these methods cannot producea set point torque within a single sampling period.

[0012] Patent application EP 1 045 514 discloses a method of controllinga rotating electrical machine using a discrete model of the machine andthe power supply inverter of the machine, the model providing thecontrol voltage to be applied to the machine by the inverter to achievea set point torque and a set point magnetic flux modulus. However, themodel is suitable for asynchronous rotating machines, and cannot beapplied to any rotating machine regardless of its type. Furthermore,regulating the torque and the flux modulus does not take intoconsideration all the operating parameters of the machine. As a resultof all this, the dynamic performance of the machine still has room forimprovement.

SUMMARY OF THE INVENTION

[0013] An object of the invention is to overcome the drawbackspreviously cited. That objective is achieved by providing a method ofregulating a rotating electrical machine receiving as input a discretecontrol voltage determined to slave the electromagnetic torque deliveredby the machine to a set point torque, said method consisting ofdetermining at each sampling time k−1 the discrete control voltage to beapplied to the machine as a function of at least one sampled signalrepresenting the electromagnetic torque of the machine, so that the setpoint torque is reached at the next sampling time k, which methodincludes:

[0014] a preparatory step of determining a discrete voltage control lawof the machine, in which the discrete control voltage to be applied ateach sampling time k is determined in the form of a first termcorresponding to free evolution of the state of the machine in theabsence of control, between the preceding sampling time k−1 and thecurrent sampling time, and a second term dependent on the set pointtorque and a set point for the magnetic energy consumed by the machine,and

[0015] at each sampling time, a step of determining, with the aid of thediscrete control law, the control voltage to be applied to the machinefor the torque of the machine to reach the set point torque and themagnetic energy consumed by the machine to correspond to the set pointmagnetic energy.

[0016] The set point energy is advantageously a minimum energy.

[0017] According to one feature of the invention the discrete controllaw determined during the preparatory step is of the form:

{right arrow over (V)} _(s,k−1) ={right arrow over (f)}(ΔΓ_(k) ,ΔW _(k))

[0018] in which f is a function giving the control voltage to be appliedat sampling time k−1 to reach the set point torque and energy as afunction of variables ΔΓ_(k) and ΔW_(k) respectively representing thedifference between the electromagnetic torque of the machine to bereached at the next sampling time k and the free evolution component ofsaid torque at said time and the difference between the magnetic energyconsumed by the machine at time k and the free evolution component ofsaid energy at said time.

[0019] According to another feature of the invention the discretecontrol law is determined in a system of axes ({tilde over (d)}, {tildeover (q)}) fixed with respect to the free evolution in discrete time ofthe rotor flux of the machine.

[0020] If the machine is a synchronous machine with smooth poles thediscrete control law determined during the preparatory step is of thefollowing form: $\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = {\frac{1}{a{{\overset{arrow}{\Phi}}_{k}^{0}}}\quad\begin{bmatrix}{\Delta \quad W} \\{\Delta \quad \Gamma}\end{bmatrix}}_{k}$

[0021] in which V_({tilde over (d)},k−1) and V_({tilde over (q)},k−1)represent the components of the control voltage vector at time k−1,expressed in a system of axes ({tilde over (d)}, {tilde over (q)}) thatis mobile in discrete time and fixed with respect to the free evolution{right arrow over (Φ)}_(k) ⁰ of the rotor flux in the machine at thenext sampling time k, ∥{right arrow over (Φ)}_(k) ⁰∥ corresponds to themodulus of the free evolution of the rotor flux at the next timesampling k, ΔΓ_(k) and ΔW_(k) respectively representing the differencebetween the electromagnetic torque of the machine to be reached at thenext sampling time k and the component of free evolution of said torqueat said time and the difference between the magnetic energy consumed bythe machine at the sampling time k and the component of free evolutionof said energy at said time.

[0022] The machine is advantageously a synchronous machine withsurface-mounted permanent magnets.

[0023] Alternatively the machine is a synchronous machine with woundsmooth poles.

[0024] According to one feature of the invention, when the machine isrotating at a speed less than a predefined threshold, the methodincludes implementing a low-speed strategy consisting of determining thecontrol voltage to be applied to the machine to reach the set pointtorque at the next sampling time with zero magnetic energy input.

[0025] The low-speed strategy preferably consists of applying thefollowing discrete control law: $\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = \begin{bmatrix}\frac{- I_{k,\overset{\sim}{d}}^{0}}{a} \\\frac{{\Delta\Gamma}_{k}}{a{{\overset{arrow}{\Phi}}_{k}^{0}}}\end{bmatrix}$

[0026] in which I_(k,{tilde over (d)}) ⁰ is the component of the freeevolution of the stator current along the axis {tilde over (d)} of thesystem of axes fixed with respect to the free evolution of the rotorflux during the sampling period between the sampling times k−1 and k.

[0027] According to another feature of the invention, when the machineis rotating at a speed greater than a predefined threshold, the methodincludes using a high-speed strategy consisting of taking account oflimitations of the inverter to determine an intermediate set pointtorque that the machine can reach at the next sampling time with a givenconsumption of magnetic energy.

[0028] The high-speed strategy preferably includes solving the followingsystem of equations:${( {I_{k,\overset{\sim}{d}} - I_{k,\overset{\sim}{d}}^{0}} )^{2} + ( {I_{k,\overset{\sim}{q}} - I_{k,\overset{\sim}{q}}^{0}} )^{2}} = ( {a{{\overset{arrow}{V}}_{s\quad \max}}} )^{2}$${I_{k,\overset{\sim}{d}}^{2} + I_{k,\overset{\sim}{q}}^{2}} = {{\overset{arrow}{I}}_{s\quad \max}}^{2}$

[0029] in which I_(k,{tilde over (k)}) and I_(k,{tilde over (q)}) arethe components of the stator current in the system of axes ({tilde over(d)},{tilde over (q)}) at the time k, I_(k,{tilde over (d)}) ⁰ andI_(k,{tilde over (q)}) ⁰ are the components of the free evolution of thestator current in said system of axes at the same time, ∥{right arrowover (V)}_(smax)∥ and ∥{right arrow over (I)}_(smax)∥ are respectivelythe moduli of the maximum voltage and the maximum current in the stator,and “a” is a constant, the control voltage being obtained with the aidof the following equation $\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = {\begin{bmatrix}\frac{I_{k,\overset{\sim}{d}} - I_{k,\overset{\sim}{d}}^{0}}{a} \\\frac{I_{k,\overset{\sim}{q}} - I_{k,\overset{\sim}{q}}^{0}}{a}\end{bmatrix}.}$

[0030] The invention also provides a regulator for a rotating machine,including an inverter fed with a power supply voltage, a regulatorreceiving as input a set point electromagnetic torque and at least onesampled signal representing the electromagnetic torque of the machineand supplying to the inverter a control signal adapted to slave theelectromagnetic torque of the machine to the set point torque bypredicting, at each sampling time, the electromagnetic torque at thenext sampling time and consecutively modifying the control voltage,which regulator includes:

[0031] a discrete control law for the machine, stored in memory, saidcontrol law giving the discrete control voltage to be applied to themachine at a current sampling time k in the form of a first termcorresponding to the free evolution of the state of the machine in theabsence of control between the preceding sampling time k−1 and thecurrent sampling time k and a second term dependent on the set pointtorque and a set point for the magnetic energy consumed by the machine,and

[0032] means for determining at each sampling time, with the aid of thediscrete control law, the control voltage to be applied to the machineso that the electromagnetic torque of the machine reaches the set pointtorque and the magnetic energy consumed by the machine corresponds tothe set point energy.

[0033] A preferred embodiment of the invention is described hereinafterby way of non-limiting example and with reference to the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0034]FIG. 1 is a block diagram of a power supply device of a rotatingmachine conforming to the invention.

[0035]FIG. 2 shows a rotating systems of axes used by the invention tomodel the operation of the rotating machine.

[0036]FIG. 3 shows a control strategy conforming to the invention foruse when the machine is operating at a low speed.

[0037]FIG. 4 is a curve of the electromagnetic torque of the machine asa function of time.

[0038]FIG. 5 shows to a larger scale a portion of the curve shown inFIG. 5 when the machine is operating at a low speed.

[0039]FIGS. 6 and 7 show a control strategy conforming to the inventionfor use when the machine when operating at a low speed.

[0040]FIG. 8 shows to a larger scale a portion of the curve shown inFIG. 5 when the machine is operating at a high speed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0041]FIG. 1 shows a rotating machine 1 consisting of a three-phasesynchronous electric motor, for example, used to drive an electricalrail vehicle, a robot or a machine tool. The rotating machine 1 issupplied with power by a power supply device 2 which includes, in theconventional way, a voltage inverter supplying power to the motor 1 byway of a three-phase alternating current voltage; the inverter isconnected to a direct current voltage power supply, with a supplyvoltage of the order of 1 500 V to 3 000 V in the case of a railtraction application, for example.

[0042] The inverter 2 is controlled by a regulator 3 which is designedto deliver a control voltage V_(ref) which determines the voltage to beapplied to the machine 1 by the inverter 2, this voltage being producedby the regulator 3 in order to slave the electromagnetic torque of themachine 1 to a set point electromagnetic torque Γ*.

[0043] As can be seen in FIG. 1, the regulator 3 also receives as inputone or more sampled signals, preferably the signals {right arrow over(I)}_(k), {right arrow over (Φ)}_(k), {right arrow over (Ω)}_(k)respectively corresponding to discrete values of the stator currentvector, the magnetic flux vector and the rotation speed of the rotor ofthe machine 1; these signals, representing the electromagnetic torque ofthe machine, are produced by a sampler observer 4 from continuoussignals I_(S1)(t), I_(S2)(t) and ω(t) measured at the motor input andoutput and respectively corresponding to two phases of the statorcurrent and a rotor rotation mechanical speed measurement signaldelivered by appropriate sensors with which the machine 1 is equipped.The two measured phases of the stator current are used to deduce thethird phase, assuming that the machine is balanced. The three phases arethen used to determine the components I_(α), I_(β)) of a stator currentvector expressed in a two-dimensional system of axes fixed with respectto the stator of the machine 1.

[0044] In the conventional way, to slave the electromagnetic torque ofthe machine 1 to the set point torque Γ* received as input, theregulator 3 uses software stored in memory to predict at each samplingtime the electromagnetic torque at the next sampling time, and modifiesaccordingly the control voltage V_(ref) to be synthesized by theinverter 2, and which is applied to the machine, to obtain the torquesimposed by the set points.

[0045] The regulator 3 is preferably a “stack response” regulator, i.e.it modifies the control voltage V_(ref) to produce the set points at thenext sampling time.

[0046] To this end, the regulator 3 includes a first stage 32, whichstores in memory a discrete model of the rotating machine 1, enablingthe change in the state of the machine between two sampling times to becomputed, and a second stage 31, which computes the control voltageV_(ref) as a function of the change in the state of the machinepredicted by the first stage 32 and the set point signal Γ* at the inputof the second stage 31.

[0047] The remainder of the description first describes the method ofcomputing the discrete model of the rotating machine 1 and then themethod of computing the control voltage V_(ref).

[0048] As previously mentioned, the dynamic behavior of the rotatingmachine 1 is modeled by a continuous time differential algebraic system.

[0049] The machine can be modeled by the following equations:

{right arrow over (X)}=A(Ω){right arrow over (X)}+B{right arrow over(V)} _(S)  (1)

{right arrow over (Y)}=h({right arrow over (X)})  (2)

[0050] in which:

[0051] {right arrow over (X)} is a state vector modeling the operationof the machine 1, and is defined by the equation${\overset{.}{\overset{arrow}{X}} = \frac{\overset{arrow}{X}}{t}},$

[0052] {right arrow over (V)}_(S) represents the vector of the voltageapplied to the input of the machine, which is equal to the statorvoltage of the machine,

[0053] A(Ω) is a state matrix dependent on the mechanical speed Ω,

[0054] B is an input matrix of the voltage vector,

[0055] {right arrow over (Y)} is an output vector including theelectromagnetic torque Γ, and

[0056] h is a non-linear function.

[0057] The above equation assumes that the relation between the controlvoltage V_(ref) and the stator voltage {right arrow over (V)}_(S) isknown, depending entirely on the characteristics of the inverter.

[0058] In the case of a synchronous motor, the state vector {right arrowover (X)} can be defined by the components of the stator current and bythe components of the rotor flux, as follows: $\begin{matrix}{\overset{arrow}{X} = {\begin{bmatrix}{\overset{arrow}{I}}_{s} \\\overset{arrow}{\Phi}\end{bmatrix}\begin{bmatrix}I_{s\quad \alpha} \\I_{s\quad \beta} \\\Phi_{\alpha} \\\Phi_{\beta}\end{bmatrix}}} & (3)\end{matrix}$

[0059] where the components of the stator current and the rotor flux areexpressed in a system of axes (α, β) fixed with respect to the stator ofthe machine 1, for example.

[0060] According to the invention, the output vector {right arrow over(Y)} defined by equation (2) has the electromagnetic torque of the motorand the magnetic energy as components. It is written as follows:$\begin{matrix}{\overset{arrow}{Y} = {\begin{bmatrix}y_{1} \\y_{2}\end{bmatrix} = {\begin{bmatrix}W \\\Gamma\end{bmatrix} = \begin{bmatrix}{\overset{arrow}{\Phi} \cdot {\overset{arrow}{I}}_{s}} \\{n_{p}\overset{arrow}{\Phi} \times {\overset{arrow}{I}}_{s}}\end{bmatrix}}}} & (4)\end{matrix}$

[0061] in which the operator “x” represents the vector product and theoperator “·” represents the scalar product.

[0062] It will be noted that in the foregoing description the statorvoltage {right arrow over (V)}_(S) can be considered to be constantbetween two successive sampling periods.

[0063] The state equation (1) can be converted into a discrete form asfollows:

{right arrow over (X)} _(k) =F(Ω_(k−1)){right arrow over (X)} _(k−1)+G(Ω_(k−1)){right arrow over (V)} _(s,k−1)  (5)

[0064] with F(Ω)=e^(A(Ω)δ) and G(Ω)=A⁻¹(Ω)[e^(A(Ω)δ)−1]B, {right arrowover (X)}_(k), {right arrow over (V)}_(S,k) and Ω_(k) respectivelyrepresenting the discrete values of the state vector {right arrow over(X)}, the stator voltage {right arrow over (V)}_(S) and the mechanicalspeed Ω_(k) of the motor at sampling time k, and δ representing thesampling period. It is assumed in the following description that themechanical speed Ω_(k) of the motor is constant during each samplingperiod.

[0065] The matrices F and G can be represented in the following manner:$\begin{matrix}{F = {{\begin{bmatrix}F_{1} & F_{2} \\F_{3} & F_{4}\end{bmatrix}\quad {and}\quad G} = \begin{bmatrix}G_{1} \\G_{2}\end{bmatrix}}} & (6)\end{matrix}$

[0066] Equation (5) is therefore written in the following manner:$\begin{matrix}{{\overset{arrow}{X}}_{k} = {\begin{bmatrix}\overset{arrow}{I} \\\overset{arrow}{\Phi}\end{bmatrix}_{k} = {{\begin{bmatrix}F_{1} & F_{2} \\F_{3} & F_{4}\end{bmatrix}\begin{bmatrix}\overset{arrow}{I} \\\overset{arrow}{\Phi}\end{bmatrix}}_{k - 1} + {\begin{bmatrix}G_{1} \\G_{2}\end{bmatrix}\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}}_{k - 1}}}} & (7)\end{matrix}$

[0067] The state vector {right arrow over (X)}_(k) can therefore bedivided into a portion which evolves freely, i.e. in the absence of anyvoltage control, and a portion due to the control voltage {right arrowover (V)}_(S,k) applied to the machine: $\begin{matrix}{{{\overset{arrow}{X}}_{k} = {{\overset{arrow}{X}}_{k}^{0} + {G\quad {\overset{arrow}{V}}_{s,{k - 1}}}}}\text{or:}} & (8) \\{\begin{bmatrix}\overset{arrow}{I} \\\overset{arrow}{\Phi}\end{bmatrix}_{k} = {\begin{bmatrix}{\overset{arrow}{I}}^{0} \\{\overset{arrow}{\Phi}}^{0}\end{bmatrix}_{k} + {G\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}}_{k - 1}}} & (9)\end{matrix}$

[0068] Consequently, the free evolution of the stator current and therotor flux {right arrow over (I)}_(k) ⁰ and {right arrow over (Φ)}_(k) ⁰are written in the following manner:${\overset{->}{I}}_{k}^{0} = {{\lbrack {F_{1}\quad F_{2}} \rbrack \begin{bmatrix}\overset{->}{I} \\\overset{->}{\Phi}\end{bmatrix}}_{k - 1}{and}}$

$\begin{matrix}{{\overset{->}{\Phi}}_{k}^{0} = {\lbrack {F_{3}\quad F_{4}} \rbrack \begin{bmatrix}\overset{->}{I} \\\overset{->}{\Phi}\end{bmatrix}}_{k - 1}} & (10)\end{matrix}$

[0069] The method according to the invention then uses the aboveequations to determine a function f yielding the control voltage V_(ref)or the stator voltage to be applied at each sampling time k as afunction of variables ΔΓ_(k) and ΔW_(k) respectively representing thedifference between the electromagnetic torque of the machine to beobtained at the sampling time k and the freely evolving component ofthat torque at that time and the difference between the magnetic energyof the machine at the time k and the freely evolving component of thatenergy at that time.

[0070] A function of the above kind can be expressed in the followingmanner:

V _(s,k−1) =f(ΔΓ_(k) ,ΔW _(k))  (11)

[0071] In the case of a synchronous motor with smooth poles, for examplewith permanent magnets mounted on the surface of the rotor, or whosepoles are provided by a winding at the surface of the rotor, thematrices A(Ω), B and the vector {right arrow over (V)}_(S) take thefollowing form in the system of axes (α, β): $\begin{matrix}{{{A(\Omega)} = \begin{bmatrix}{- \frac{R_{s}}{L_{s}}} & 0 & 0 & {n_{p}\frac{\Omega}{L_{s}}} \\0 & {- \frac{R_{s}}{L_{s}}} & {{- n_{p}}\frac{\Omega}{L_{s}}} & 0 \\0 & 0 & 0 & {{- n_{p}}\Omega} \\0 & 0 & {n_{p}\Omega} & 0\end{bmatrix}},{B = \begin{bmatrix}\frac{1}{L_{s}} & 0 \\0 & \frac{1}{L_{s}} \\0 & 0 \\0 & 0\end{bmatrix}},{{\overset{->}{V}}_{s} = \begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}}} & (12)\end{matrix}$

[0072] in which R_(s) is the resistance of the stator of the motor 1,L_(s) is the inductance of the stator, and n_(p) is the number of pairsof poles of the motor.

[0073] As a result of this, the matrices F_(i) and G_(j) introduced intoequation (6) have the following values: ${F_{1} = \begin{bmatrix}e^{- \frac{\delta}{\tau_{s}}} & 0 \\0 & e^{- \frac{\delta}{\tau_{s}}}\end{bmatrix}},{F_{3} = \begin{bmatrix}0 & 0 \\0 & 0\end{bmatrix}},{F_{4} = \begin{bmatrix}{\cos \quad \theta} & {{- \sin}\quad \theta} \\{\sin \quad \theta} & {\cos \quad \theta}\end{bmatrix}},{F_{2} = {\frac{Z_{1}}{L_{s}Z_{2}^{2}}\begin{bmatrix}{{{- Z_{1}}\cos \quad \theta} + {R_{s}\sin \quad \theta} + {Z_{1}e^{- \frac{\delta}{\tau_{s}}}}} & {{Z_{1}\sin \quad \theta} + {R_{s}\cos \quad \theta} - {R_{s}e^{- \frac{\delta}{\tau_{s}}}}} \\{{{- Z_{1}}\sin \quad \theta} - {R_{s}\cos \quad \theta} + {R_{s}e^{- \frac{\delta}{\tau_{s}}}}} & {{{- Z_{1}}\cos \quad \theta} + {R_{s}\sin \quad \theta} + {Z_{1}e^{- \frac{\delta}{\tau_{s}}}}}\end{bmatrix}}}$ ${G_{1} = \begin{bmatrix}a & 0 \\0 & a\end{bmatrix}},{G_{2} = \begin{bmatrix}0 & 0 \\0 & 0\end{bmatrix}},{{{in}\quad {which}\quad Z_{1}} = {L_{s}n_{p}\Omega}},\quad {Z_{2}^{2} = {R_{s}^{2} + Z_{1}^{2}}},{\tau_{s} = \frac{L_{s}}{R_{s}}},{\theta = {\delta \quad n_{p}\Omega \quad {and}}}$$a = {\frac{1}{R_{s}}{( {1 - e^{- \frac{\delta}{\tau_{s}}}} ).}}$

[0074] Note that the above expressions do not involve the position ofthe rotor.

[0075] What is more, for the above type of motor, equation (5) iswritten in the following manner: $\begin{matrix}{{\overset{->}{X}}_{k} = {\begin{bmatrix}\overset{->}{I} \\\overset{->}{\Phi}\end{bmatrix}_{k} = {{{\begin{bmatrix}F_{1} & F_{2} \\F_{3} & F_{4}\end{bmatrix}\begin{bmatrix}\overset{->}{I} \\\overset{->}{\Phi}\end{bmatrix}}_{k - 1} + {a\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}}_{k - 1}} = {\begin{bmatrix}{\overset{->}{I}}^{0} \\{\overset{->}{\Phi}}^{0}\end{bmatrix}_{k - 1} + {a\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}}_{k - 1}}}}} & (13)\end{matrix}$

[0076] Consequently, the free evolution of the stator current and therotor flux {right arrow over (I)}_(k) and {right arrow over (Ω)}_(k) ⁰are written in the following manner: $\begin{matrix}\begin{matrix}{{\overset{->}{I}}_{k}^{0} = {{\lbrack {F_{1}\quad F_{2}} \rbrack \begin{bmatrix}\overset{->}{I} \\\overset{->}{\Phi}\end{bmatrix}}_{k - 1}\quad {and}}} \\{{\overset{->}{\Phi}}_{k}^{0} = {{\overset{->}{\Phi}}_{k} = {{\lbrack {F_{3}\quad F_{4}} \rbrack \begin{bmatrix}\overset{->}{I} \\\overset{->}{\Phi}\end{bmatrix}}_{k - 1} = {F_{4}{\overset{->}{\Phi}}_{k - 1}}}}}\end{matrix} & (14)\end{matrix}$

[0077] Furthermore, from equation (4), the electromagnetic torque isdefined by the following equation:

Γ_(k) =n _(p){right arrow over (106 )}_(k) ×{right arrow over (I)}_(k)  (15)

[0078] If the stator current and the rotor flux obtained from equation(13) are substituted in the above expression for the torque, a formulais obtained in which the torque is also divided into a freely evolvingpart and a part due to the control voltage:

Γ_(k)=Γ_(k) ⁰ +an _(p) {right arrow over (Ω)}_(k) ⁰ ×{right arrow over(V)} _(s,k−1)  (16)

[0079] the freely evolving part of the torque being equal to:

Γ_(k) ⁰ =n _(p){right arrow over (Φ)}_(k) ⁰ ×{right arrow over (I)} _(k)⁰  (17)

[0080] Consider now the quantity: $\begin{matrix}{{\Delta\Gamma}_{k} = \frac{\Gamma_{k} - \Gamma_{k}^{0}}{n_{p}}} & (18) \\{\frac{{\Delta\Gamma}_{k}}{a} = {{{\overset{->}{\Phi}}_{k}^{0} \times {\overset{->}{V}}_{{ref},{k - 1}}} = {{\Phi_{k,\alpha}^{0}v_{\beta,{k - 1}}} - {\Phi_{k,\beta}^{0}v_{\alpha,{k - 1}}}}}} & (19)\end{matrix}$

[0081] Now, from equation (14), $\begin{matrix}{{\overset{->}{\Phi}}_{k}^{0} = {{\overset{->}{\Phi}}_{k} = {{F_{4}{\overset{->}{\Phi}}_{k - 1}} = {\begin{bmatrix}{\cos \quad \theta} & {{- \sin}\quad \theta} \\{\sin \quad \theta} & {\cos \quad \theta}\end{bmatrix}{\overset{->}{\Phi}}_{k - 1}}}}} & (20)\end{matrix}$

[0082] Consequently, in the case of a synchronous motor withsurface-mounted permanent magnets, the rotor flux has a constant modulusthat is equal to the modulus of the magnetic flux ∥{right arrow over(Ω)}_(m)∥ and in each sampling period rotates through an angleθ=δn_(p)Ω. Regulation is therefore not possible on the basis of a setpoint magnetic flux modulus, as explained in patent application EP 1 045514.

[0083] As the stator voltage does not interfere with the evolution ofthe rotor flux, it is possible to consider only the torque equation inwhich the two components of the stator voltage {right arrow over(V)}_(s) in the system of axes (α, β) appear, which leaves one degree offreedom (an equation in two unknowns). As a result of this, it ispossible additionally to control another operating parameter of themotor to maximize the torque for a given stator current, taking accountof voltage and current limitations in the stator. Furthermore, aspreviously mentioned, the object of the present invention is to provide“stack response” torque control (so that Γ*=Γ_(k)) and to control themagnetic energy in the machine, which amounts to the same thing as alsocontrolling the projection of the stator current onto the rotor flux.From equation (4), the magnetic energy in the machine takes the form:

W _(k)={right arrow over (Φ)}_(k) ·{right arrow over (I)} _(k)={rightarrow over (Φ)}_(k) ⁰ ·{right arrow over (I)} _(k)  (21)

[0084] From equation (13), the stator current is given by the followingequation:

{right arrow over (I)} _(k) ={right arrow over (I)} _(k) ⁰ +a{rightarrow over (V)} _(s,k−1)  (22)

[0085] As a result of this: $\begin{matrix}{\frac{\Delta \quad W_{k}}{a} = {\frac{W_{k} - W_{k}^{0}}{a} = {\frac{{\overset{->}{\Phi}}_{k}^{0}( {{\overset{->}{I}}_{k} - {\overset{->}{I}}_{k}^{0}} )}{a} = {{{\overset{->}{\Phi}}_{k}^{0}{\overset{->}{V}}_{s,{k - 1}}} = {{\Phi_{k,\alpha}^{0}v_{\alpha,{k - 1}}} + \Phi_{k,{\beta^{v}\beta},{k - 1}}^{0}}}}}} & (23)\end{matrix}$

[0086] The control law for the voltage V_(S) can then be deduced fromequations (19) and (23): $\begin{matrix}\{ \begin{matrix}{v_{\alpha,{k - 1}} = \frac{{\Phi_{k,\alpha}^{0}( {{\Phi_{k,\alpha}^{0}( {I_{k,\alpha} - I_{k,\alpha}^{0}} )} + {\Phi_{k,\beta}^{0}( {I_{k,\beta} - I_{k,\beta}^{0}} )}} )} - {\Delta\Gamma\Phi}_{k,\beta}^{0}}{a{{\overset{->}{\Phi}}_{m}}^{2}}} \\{v_{\beta,{k - 1}} = \frac{{\Phi_{k,\beta}^{0}( {{\Phi_{k,\alpha}^{0}( {I_{k,\alpha} - I_{k,\alpha}^{0}} )} + {\Phi_{k,\beta}^{0}( {I_{k,\beta} - I_{k,\beta}^{0}} )}} )} + {\Delta\Gamma\Phi}_{k,\alpha}^{0}}{a{{\overset{->}{\Phi}}_{m}}^{2}}}\end{matrix}  & (24)\end{matrix}$

[0087] The above control law can also be expressed in the followingmanner in the system of axes (α, β): $\begin{matrix}{\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}_{k - 1} = {{\frac{1}{{{\overset{->}{\Phi}}_{m}}^{2}}\begin{bmatrix}\Phi_{\alpha}^{0} & {- \Phi_{\beta}^{0}} \\\Phi_{\beta}^{0} & \Phi_{\alpha}^{0}\end{bmatrix}}_{k}{\frac{1}{a}\begin{bmatrix}{\Delta \quad W_{k}} \\{\Delta \quad \Gamma_{k}}\end{bmatrix}}}} & (25)\end{matrix}$

[0088] Consider now the following rotation matrix R: $\begin{matrix}{{R( \rho_{k}^{0} )} = {\begin{bmatrix}\frac{\Phi_{\alpha}^{0}}{{\overset{->}{\Phi}}_{m}} & \frac{\Phi_{\beta}^{0}}{{\overset{->}{\Phi}}_{m}} \\{- \frac{\Phi_{\beta}^{0}}{{\overset{->}{\Phi}}_{m}}} & \frac{\Phi_{\alpha}^{0}}{{\overset{->}{\Phi}}_{m}}\end{bmatrix}_{k} = \begin{bmatrix}{\cos ( \rho^{0} )} & {\sin ( \rho^{0} )} \\{- {\sin ( \rho^{0} )}} & {\cos ( \rho^{0} )}\end{bmatrix}_{k}}} & (26)\end{matrix}$

[0089] The control law can then be written as follows: $\begin{matrix}{\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}_{k - 1} = {\frac{1}{{\overset{->}{\Phi}}_{m}}{R^{- 1}( \rho_{k}^{0} )}{\frac{1}{a}\begin{bmatrix}{\Delta \quad W} \\{\Delta \quad \Gamma}\end{bmatrix}}_{k}}} & (27)\end{matrix}$

[0090] The regulator 3 therefore has the specific feature of being basedon free evolution of the direction of the rotor flux, as shown in FIG.2. If the reference system of axes is now changed, to a system of axes({tilde over (d)}, {tilde over (q)}) fixed with respect to the freeevolution of the rotor flux, the previous equation is written in thefollowing very simple form: $\begin{matrix}{\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = {{\frac{1}{a{{\overset{->}{\Phi}}_{k}^{0}}}\begin{bmatrix}{\Delta \quad W} \\{\Delta \quad \Gamma}\end{bmatrix}}_{k} = \begin{bmatrix}\frac{I_{k,\overset{\sim}{d}} - I_{k,\overset{\sim}{d}}^{0}}{a} \\\frac{I_{k,\overset{\sim}{q}} - I_{k,\overset{\sim}{q}}^{0}}{a}\end{bmatrix}}} & (28)\end{matrix}$

[0091] The above equation expresses the voltage that must be applied asinput to the inverter 3 at the sampling time k−1 to obtain the requiredtorque variation at the next sampling time k. Note that there is perfectdecoupling between torque control and magnetic energy control (anglebetween the rotor flux and stator current vectors and the modulus of thestator current vector), V_({tilde over (q)}) depending only on thevariation of the electromagnetic torque of the machine 1.

[0092] Note also that the system of axes ({tilde over (d)}, {tilde over(q)}), which is fixed with respect to the discrete rotor flux, turnsstepwise at each sampling time and is equivalent to the system of axes(d, q) of the standard continuous model.

[0093] In the final analysis, thanks to the change to discrete time asearly as modeling the state of the machine, and by an appropriate choiceof the system of axes, there is very surprisingly obtained a very simplemodel for synchronous motors with smooth poles. In the case of a motorin which the smooth poles of the rotor consist of windings, theamplitude of the magnetic or rotor flux can also be controlled.

[0094] Various control strategies can be applied depending on the speedΩ of the motor.

[0095] At a low speed Ω the torque is a maximum for a given current andzero magnetic energy W. This signifies that the stator current is inquadrature with the rotor or magnetic flux. On the other hand, when themotor is rotating at a speed beyond a particular limit, the availabletorque is progressively reduced, but the power supplied by the machineis at a maximum. The magnetic energy consumed can then no longer bezero. This speed limitation for a given torque is due in particular toinverter current and voltage limitations.

[0096] The strategy to be applied at a low speed is shown in FIG. 3.FIG. 3 shows the various vectors involved in the state equation (1),namely: $\begin{matrix}{\frac{{\overset{->}{I}}_{s}}{t} = {{\frac{R_{s}}{L_{s}}{\overset{->}{I}}_{s}} + {n_{p}{\frac{\Omega}{L_{s}}\begin{bmatrix}0 & 1 \\{- 1} & 0\end{bmatrix}}\overset{->}{\Phi}} + {\frac{1}{L_{s}}{\overset{->}{V}}_{s}}}} & (29)\end{matrix}$

[0097] whence: $\begin{matrix}\begin{matrix}{{\overset{->}{V}}_{s} = {{L_{s}\frac{{\overset{->}{I}}_{s}}{t}} = {{R_{s}{\overset{->}{I}}_{s}} + \underset{}{n_{p}{\Omega \begin{bmatrix}0 & {- 1} \\1 & 0\end{bmatrix}}\overset{->}{\Phi}}}}} \\{= {{L_{s}\frac{{\overset{->}{I}}_{s}}{t}} = {{R_{s}{\overset{->}{I}}_{s}} + {\overset{->}{V}}_{f}}}}\end{matrix} & (30)\end{matrix}$

[0098] Note that the vector V_(f) is perpendicular to the flux vector{right arrow over (Φ)} and therefore parallel to the current vector{right arrow over (I)}_(S).

[0099] For a given speed and a given set point torque, if the modulus ofthe stator voltage computed by the regulator 3 is less than the voltage{right arrow over (V)}_(S) supplied by the inverter, the controlstrategy can consist of forcing the component I_(k,{tilde over (d)}) tozero so that the stator current and the rotor flux are in quadrature.This yields the following control law: $\begin{matrix}{\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = \begin{bmatrix}\frac{- I_{k,\overset{\sim}{d}}^{0}}{a} \\\frac{{\Delta\Gamma}_{k}}{a{{\overset{->}{\Phi}}_{k}^{0}}}\end{bmatrix}} & (31)\end{matrix}$

[0100] in which I_(k,{tilde over (d)}) ⁰ is given by the equations (14).

[0101]FIG. 4 shows one example of a curve of the evolution of the torquedemanded from the motor as a function of time. The curve shows inparticular that at time t=1.5 s the torque has changed from −35 Nm to+25 Nm. Refer now to the curve shown in FIG. 5, which shows in moredetail how the torque is changing at about this time, when the motor isrotating at a low speed; it can be seen that the torque has changed fromthe first value to the second value within a sampling period, i.e.within 1 ms.

[0102] At a high speed, for a given set point torque, and if thecorresponding control voltage is greater than the voltage {right arrowover (V)}_(S) that the inverter 2 can supply, the preceding strategycannot be applied. It is therefore necessary to limit the stator voltageby reducing the stator flux, which is given by the following equation:

{right arrow over (Φ)}_(s)={right arrow over (Φ)}_(k) +L _(s) {rightarrow over (I)} _(k)  (32)

[0103] Because the rotor flux is constant, the stator flux can bereduced by modifying the modulus of the stator current and the anglebetween the stator current vector and the magnetic flux, as shown inFIG. 6

[0104] The control strategy at high speeds is shown in FIG. 6, in whichthe stator current and the rotor flux can no longer be in quadrature; inthis case the stator flux can in part be compensated by the componentI_(k,{tilde over (d)}) of the stator current.

[0105] This strategy assumes that the stator voltage is at a maximum,that is to say: $\begin{matrix}{{v_{\overset{\sim}{d}}^{2} + v_{\overset{\sim}{q}}^{2}} = {{\overset{->}{V}}_{s\quad \max}}^{2}} & (33)\end{matrix}$

[0106] The following equation is obtained from the previous equation andequation (28):

(I _(k,{tilde over (d)}) −I _(k,{tilde over (d)}) ⁰)²=(a∥{right arrowover (V)} _(smax)∥)²  (34)

[0107] It is also assumed that the stator current is at a maximum, i.e.that:

I _(k,{tilde over (d)}) ² +I _(k,{tilde over (q)}) ² =∥I _(smax)∥²  (35)

[0108] The last two equations are the equations of two circles, thefirst circle 21 (see FIG. 7) being centered on the end of the vector{right arrow over (I)}_(k) ⁰ and having a radius equal to a∥{right arrowover (V)}_(smax)∥, and the second circle 22 being centered on the originof the system of axes ({tilde over (d)}, {tilde over (q)}) having aradius equal to ∥{right arrow over (I)}_(smax)∥².

[0109] Both equations (34) and (35) are therefore satisfied at theintersection points 23 and 24 of the two circles. In fact, only one ofthese two points (the point 23) is the optimum for controlling themachine, i.e. the one that corresponds to a stator current componentI_(k,{tilde over (d)}) on the axis {tilde over (d)} which is negative toreduce the stator flux. The value of that component can be obtained fromequation (35):

I _(k,{tilde over (d)}) =−{square root}{square root over (∥I)} _(smax)∥²−I _(k,{tilde over (q)}) ²  (36)

[0110] Furthermore, the area delimited by the intersection of the twocircles 21 and 22 corresponds to the possible stator current and voltagevalues. Consequently, a set point torque can be obtained within a singlesampling period if the following condition, resulting from equations(28) and (34), is satisfied: $\begin{matrix}{{( \frac{{\Delta\Gamma}_{k}}{{\overset{->}{\Phi}}_{m}} )^{2} \leq {{a^{2}{{\overset{->}{V}}_{s\quad \max}}^{2}} - ( {I_{k,\overset{\sim}{d}} - I_{k,\overset{\sim}{d}}^{0}} )^{2}}}{{or}:}} & (37) \\{I_{k,\overset{\sim}{d}}^{2} \leq {{{\overset{->}{I}}_{s\quad \max}}^{2} - ( {\frac{\Delta\Gamma}{{\overset{->}{\Phi}}_{p}^{0}} + I_{k,\overset{\sim}{q}}^{0}} )^{2}}} & (38)\end{matrix}$

[0111] This second condition is the result of equations (28) and (35).

[0112] In FIG. 8, which is to a larger scale, it can be seen that atorque of 25 Nm is achieved within seven sampling periods, i.e. within 7ms, by applying intermediate set point torques in each sampling period.

[0113] Note that the equations that model the operation of the motor 1and the inverter 2 conforming to the invention are very simple and arenot the result of approximations. They can therefore be implementedusing relatively modest computation means. What is more, these equationsdo not necessitate a knowledge of the position of the rotor relative tothe stator in each sampling period.

There is claimed:
 1. A method of regulating a rotating electricalmachine receiving as input a discrete control voltage determined toslave the electromagnetic torque delivered by said machine to a setpoint torque, said method consisting of determining at each samplingtime said discrete control voltage to be applied to said machine as afunction of at least one sampled signal representing the electromagnetictorque of said machine, so that the set point torque is reached at thenext sampling time, which method includes a preparatory step ofdetermining a discrete voltage control law of said machine in which saiddiscrete control voltage to be applied at each sampling time isdetermined in the form of a first term corresponding to free evolutionof the state of said machine in the absence of control, between thepreceding sampling time and the current sampling time, and a second termdependent on said set point torque and a set point for the magneticenergy consumed by said machine, and, at each sampling time, a step ofdetermining, with the aid of said discrete control law, the controlvoltage to be applied to said machine for the torque of said machine toreach said set point torque and the magnetic energy consumed by saidmachine to correspond to said set point magnetic energy.
 2. Theregulation method claimed in claim 1, wherein said set point energy is aminimum energy.
 3. The regulation method claimed in claim 1, whereinsaid discrete control law determined during said preparatory step is ofthe form: {right arrow over (V)} _(s,k−1) ={right arrow over (f)}(ΔΓ_(k),ΔW _(k)) in which f is a function giving said control voltage to beapplied at sampling time k−1 to reach said set point torque and energyas a function of variables ΔΓ_(k) and ΔW_(k) respectively representingthe difference between said electromagnetic torque of said machine to bereached at said next sampling time and said free evolution component ofsaid torque at said time and the difference between the magnetic energyconsumed by said machine at time k and said free evolution component ofsaid energy at said time.
 4. The regulation method claimed in claim 1,wherein said discrete control law is determined in a system of axesfixed with respect to said free evolution in discrete time of said rotorflux of said machine.
 5. The regulation method claimed in claim 1,wherein said machine is a synchronous machine with smooth poles and saiddiscrete control law determined during said preparatory step is of thefollowing form: $\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = {\frac{1}{a{{\overset{->}{\Phi}}_{k}^{0}}}\begin{bmatrix}{\Delta \quad W} \\{\Delta \quad \Gamma}\end{bmatrix}}_{k}$

in which v_({tilde over (d)},k−1) and v_({tilde over (q)},k−1) representthe components of the control voltage vector at time k−1, expressed in asystem of axes ({tilde over (d)}, {tilde over (q)}) that is mobile indiscrete time and fixed with respect to said free evolution {right arrowover (Φ)}_(k) ⁰ of said rotor flux in said machine at said next samplingtime k, “a” is a constant, and ∥{right arrow over (Φ)}_(k) ⁰ correspondsto the modulus of said free evolution of said rotor flux at said nextsampling time k, ΔΓ_(k) and ΔW_(k) respectively representing thedifference between said electromagnetic torque of said machine to bereached at said next sampling time k and said component of freeevolution of said torque at said time and the difference between saidmagnetic energy consumed by said machine at said sampling time k andsaid component of free evolution of said energy at said time.
 6. Theregulation method claimed in claim 1, wherein said machine is asynchronous machine with surface-mounted permanent magnets.
 7. Theregulation method claimed in claim 1, wherein said machine is asynchronous machine with wound smooth poles.
 8. The regulation methodclaimed in claim 6, wherein, when said machine is rotating at a speedless than a predefined threshold, it includes implementing a low-speedstrategy consisting of determining said control voltage to be applied tosaid machine to reach said set point torque at said next sampling timewith zero magnetic energy input.
 9. The regulation method claimed inclaim 8, wherein said low-speed strategy consists of applying thefollowing discrete control law: $\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = \begin{bmatrix}\frac{- I_{k,\overset{\sim}{d}}^{0}}{a} \\\frac{\Delta \quad \Gamma_{k}}{a\quad {{\overset{arrow}{\Phi}}_{k}^{0}}}\end{bmatrix}$

in which I_(k,{tilde over (d)}) ⁰ is said component of said freeevolution of said stator current along the axis {tilde over (d)} of thesystem of axes ({tilde over (d)}, {tilde over (q)}) fixed with respectto said free evolution of said rotor flux during the sampling periodbetween said sampling times k−1 and k, “a” is a constant, ∥{right arrowover (Φ)}_(k) ⁰∥ corresponds to the modulus of said free evolution ofsaid rotor flux at said next sampling time k, and ΔΓ_(k) represents thedifference between said electromagnetic torque of said machine to bereached at said next sampling time k and said component of freeevolution of said torque at said time.
 10. The regulation method claimedin claim 6, wherein, when said machine is rotating at a speed greaterthan a predefined threshold, it includes using a high-speed strategyconsisting of taking account of limitations of said inverter todetermine an intermediate set point torque that said machine can reachat said next sampling time with a given consumption of magnetic energy.11. The regulation method claimed in claim 10, wherein said high-speedstrategy includes solving the following system of equations:${( {I_{k,\overset{\sim}{d}} - I_{k,\overset{\sim}{d}}^{0}} )^{2} + ( {I_{k,\overset{\sim}{q}} - I_{k,\overset{\sim}{q}}^{0}} )^{2}} = ( {a{{\overset{arrow}{V}}_{s\quad \max}}} )^{2}$${I_{k,\overset{\sim}{d}}^{2} + I_{k,\overset{\sim}{q}}^{2}} = {{\overset{arrow}{I}}_{s\quad \max}}^{2}$

in which I_(k,{tilde over (d)}) and I_(k,{tilde over (q)}) are thecomponents of said stator current in the system of axes ({tilde over(d)}, {tilde over (q)}) at said time k, I_(k,{tilde over (d)}) ⁰ andI_(k,{tilde over (q)}) ⁰ are the components of said free evolution ofsaid stator current in said system of axes at the same time, ∥{rightarrow over (V)}_(smax)∥ and ∥{right arrow over (I)}smax∥ arerespectively the moduli of the maximum voltage and the maximum currentin said stator, and “a” is a constant, said control voltage beingobtained with the aid of the following equation $\begin{bmatrix}v_{\overset{\sim}{d}} \\v_{\overset{\sim}{q}}\end{bmatrix}_{k - 1} = {\begin{bmatrix}\frac{I_{k,\overset{\sim}{d}} - I_{k,\overset{\sim}{d}}^{0}}{a} \\\frac{I_{k,\overset{\sim}{q}} - I_{k,\overset{\sim}{q}}^{0}}{a}\end{bmatrix}.}$


12. A regulator for a rotating machine, including an inverter, aregulator receiving as input a set point electromagnetic torque and atleast one sampled signal representing the electromagnetic torque of saidmachine and supplying to said inverter a control signal adapted to slavesaid electromagnetic torque of said machine to said set point torque bypredicting, at each sampling time, the electromagnetic torque at thenext sampling time and consecutively modifying said control voltage,which regulator includes a discrete control law for said machine, storedin memory, said control law giving said discrete control voltage to beapplied to said machine at a current sampling time in the form of afirst term corresponding to the free evolution of the state of saidmachine in the absence of control between the preceding sampling timeand said current sampling time and a second term dependent on said setpoint torque and a set point for the magnetic energy consumed by saidmachine, and means for determining, at each sampling time, with the aidof said discrete control law, said control voltage to be applied to saidmachine so that said electromagnetic torque of said machine reaches saidset point torque and the magnetic energy consumed by said machinecorresponds to said set point energy.